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Timeline of mathematics
This is a of and . Modern 16th century * 1501 – writes the . * 1520 – develops a method for solving "depressed" cubic equations (cubic equations without an x2 term), but does not publish. * 1522 – explained the use of Arabic digits and their advantages over Roman numerals. * 1535 – independently develops a method for solving depressed cubic equations but also does not publish. * 1539 – learns Tartaglia's method for solving depressed cubics and discovers a method for depressing cubics, thereby creating a method for solving all cubics. * 1540 – solves the . * 1544 – publishes Arithmetica integra. * 1545 – conceives the idea of s. * 1550 – , a mathematician, writes the , the world's first text, which gives detailed derivations of many calculus theorems and formulae. * 1572 – writes Algebra treatise and uses imaginary numbers to solve cubic equations. * 1584 – calculates . * 1596 – computes π to twenty decimal places using inscribed and circumscribed polygons. 17th century * 1614 – discusses Napierian s in Mirifici Logarithmorum Canonis Descriptio. * 1617 – discusses decimal logarithms in Logarithmorum Chilias Prima. * 1618 – John Napier publishes the first references to in a work on . * 1619 – discovers ( claimed that he also discovered it independently). * 1619 – discovers two of the . * 1629 – Pierre de Fermat develops a rudimentary . * 1634 – shows that the area under a is three times the area of its generating circle. * 1636 – jointly discovered the pair of s 9,363,584 and 9,437,056 along with (1636). * 1637 – Pierre de Fermat claims to have proven in his copy of ' Arithmetica. * 1637 – First use of the term by René Descartes; it was meant to be derogatory. * 1643 – René Descartes develops . * 1654 – and Pierre de Fermat create the theory of . * 1655 – writes Arithmetica Infinitorum. * 1658 – shows that the length of a cycloid is four times the diameter of its generating circle. * 1665 – works on the and develops his version of . * 1668 – and discover an for the logarithm while attempting to calculate the area under a . * 1671 – develops a series expansion for the inverse- function (originally discovered by ). * 1671 – James Gregory discovers . * 1673 – also develops his version of infinitesimal calculus. * 1675 – Isaac Newton invents an algorithm for the . * 1680s – Gottfried Leibniz works on symbolic logic. * 1683 – discovers the and . * 1683 – Seki Takakazu develops . * 1691 – Gottfried Leibniz discovers the technique of separation of variables for ordinary s. * 1693 – prepares the first mortality tables statistically relating death rate to age. * 1696 – states for the computation of certain . * 1696 – and solve , the first result in the . * 1699 – calculates π to 72 digits but only 71 are correct. 18th century * 1706 – develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places. * 1708 – discovers . whom the numbers are named after is believed to have independently discovered the numbers shortly after Takakazu. * 1712 – develops . * 1722 – states connecting s and s. * 1722 – introduces . * 1724 – Abraham De Moivre studies mortality statistics and the foundation of the theory of annuities in Annuities on Lives. * 1730 – publishes The Differential Method. * 1733 – studies what geometry would be like if were false. * 1733 – Abraham de Moivre introduces the to approximate the in probability. * 1734 – introduces the for solving first-order ordinary s. * 1735 – Leonhard Euler solves the , relating an infinite series to π. * 1736 – Leonhard Euler solves the problem of the , in effect creating . * 1739 – Leonhard Euler solves the general with . * 1742 – conjectures that every even number greater than two can be expressed as the sum of two primes, now known as . * 1747 – the problem (one-dimensional ). * 1748 – discusses analysis in Instituzioni Analitiche ad Uso della Gioventu Italiana. * 1761 – proves . * 1761 – proves that π is irrational. * 1762 – discovers the . * 1789 – improves Machin's formula and computes π to 140 decimal places, 136 of which were correct. * 1794 – Jurij Vega publishes . * 1796 – proves that the can be constructed using only a . * 1796 – conjectures the . * 1797 – associates vectors with complex numbers and studies complex number operations in geometrical terms. * 1799 – Carl Friedrich Gauss proves the (every polynomial equation has a solution among the complex numbers). * 1799 – partially proves the that or higher equations cannot be solved by a general formula. 19th century * 1801 – , Carl Friedrich Gauss's treatise, is published in Latin. * 1805 – Adrien-Marie Legendre introduces the for fitting a curve to a given set of observations. * 1806 – discovers the two remaining . * 1806 – publishes proof of the and the . * 1807 – announces his discoveries about the . * 1811 – Carl Friedrich Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration. * 1815 – carries out integrations along paths in the complex plane. * 1817 – presents the —a that is negative at one point and positive at another point must be zero for at least one point in between. Bolzano gives a first formal . * 1821 – publishes which purportedly contains an erroneous “proof” that the of continuous functions is continuous. * 1822 – presents the for integration around the boundary of a rectangle in the . * 1822 – Irisawa Shintarō Hiroatsu analyzes in a . * 1823 - is published in the second edition of Essai sur la théorie des nombres * 1824 – partially proves the that the general or higher equations cannot be solved by a general formula involving only arithmetical operations and roots. * 1825 – Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths—he assumes the function being integrated has a continuous derivative, and he introduces the theory of s in . * 1825 – and Adrien-Marie Legendre prove Fermat's Last Theorem for n'' = 5. * 1825 – discovers . * 1826 – gives counterexamples to ’s purported “proof” that the of continuous functions is continuous. * 1828 – George Green proves . * 1829 – , , and invent hyperbolic . * 1831 – rediscovers and gives the first proof of the divergence theorem earlier described by Lagrange, Gauss and Green. * 1832 – presents a general condition for the solvability of s, thereby essentially founding and . * 1832 – Lejeune Dirichlet proves Fermat's Last Theorem for ''n = 14. * 1835 – Lejeune Dirichlet proves about prime numbers in arithmetical progressions. * 1837 – proves that doubling the cube and are impossible with only a compass and straightedge, as well as the full completion of the problem of constructability of regular polygons. * 1837 – develops . * 1838 – First mention of in a paper by ; later formalized by . Uniform convergence is required to fix erroneous “proof” that the of continuous functions is continuous from Cauchy’s 1821 . * 1841 – discovers but does not publish the . * 1843 – discovers and presents the Laurent expansion theorem. * 1843 – discovers the calculus of s and deduces that they are non-commutative. * 1847 – formalizes in The Mathematical Analysis of Logic, defining what is now called . * 1849 – shows that s can arise from a combination of periodic waves. * 1850 – distinguishes between poles and branch points and introduces the concept of . * 1850 – George Gabriel Stokes rediscovers and proves Stokes' theorem. * 1854 – introduces . * 1854 – shows that quaternions can be used to represent rotations in four-dimensional . * 1858 – invents the . * 1858 – solves the general quintic equation by means of elliptic and modular functions. * 1859 – Bernhard Riemann formulates the , which has strong implications about the distribution of s. * 1868 – demonstrates of ’s from the other axioms of . * 1870 – constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate. * 1872 – invents what is now called the Dedekind Cut for defining irrational numbers, and now used for defining surreal numbers. * 1873 – proves that is . * 1873 – presents his method for finding series solutions to linear differential equations with s. * 1874 – proves that the set of all s is but the set of all real s is . does not use his , which he published in 1891. * 1882 – proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge. * 1882 – Felix Klein invents the . * 1895 – and derive the to describe the development of long solitary water waves in a canal of rectangular cross section. * 1895 – Georg Cantor publishes a book about set theory containing the arithmetic of infinite s and the . * 1895 – publishes paper " " which started modern topology. * 1896 – and independently prove the . * 1896 – presents Geometry of numbers. * 1899 – Georg Cantor discovers a contradiction in his set theory. * 1899 – presents a set of self-consistent geometric axioms in Foundations of Geometry. * 1900 – David Hilbert states his , which show where some further mathematical work is needed. Contemporary 20th century * 1901 – develops the . * 1901 – publishes on . * 1903 – presents a algorithm * 1903 – gives considerably simpler proof of the prime number theorem. * 1908 – axiomizes , thus avoiding Cantor's contradictions. * 1908 – solves the Riemann problem about the existence of a differential equation with a given and uses Sokhotsky – Plemelj formulae. * 1912 – presents the . * 1912 – Josip Plemelj publishes simplified proof for the Fermat's Last Theorem for exponent n'' = 5. * 1915 – proves , which shows that every has a corresponding . * 1916 – introduces . This conjecture is later generalized by . * 1919 – defines ''B''2 for s. * 1921 – Emmy Noether introduces the first general definition of a . * 1928 – begins devising the principles of and proves the . * 1929 – Emmy Noether introduces the first general representation theory of groups and algebras. * 1930 – shows that the has no solution. * 1930 – introduces . * 1931 – proves , which shows that every axiomatic system for mathematics is either incomplete or inconsistent. * 1931 – develops theorems in and es. * 1933 – and present the . * 1933 – publishes his book ''Basic notions of the calculus of probability (Grundbegriffe der Wahrscheinlichkeitsrechnung), which contains an based on . * 1938 - introduces . * 1940 – Kurt Gödel shows that neither the nor the can be disproven from the standard axioms of set theory. * 1942 – and develop a algorithm. * 1943 – proposes a method for nonlinear least squares fitting. * 1945 – introduces . * 1945 – and start . * 1945 – and give the for (co-)homology. * 1946 – introduces the . * 1948 – John von Neumann mathematically studies .I * 1948 - and prove independently in an elementary way the . * 1949 – and L.R. Smith compute π to 2,037 decimal places using . * 1949 – develops notion of . * 1950 – and John von Neumann present dynamical systems. * 1953 – introduces the idea of thermodynamic algorithms. * 1955 – et al. publish the complete list of . * 1955 – , , Stanisław Ulam, and numerically study a nonlinear spring model of heat conduction and discover solitary wave type behavior. * 1956 – describes a of s. * 1956 – discovers the existence of an in seven dimensions, inaugurating the field of . * 1957 – develops . * 1957 – provides the for crease-free . * 1958 – 's proof of the is published. * 1959 – creates . * 1960 – invents the algorithm. * 1960 – and present the . * 1961 – and compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer. * 1961 – and independently develop the to calculate the and of a matrix. * 1961 – Stephen Smale proves the for all dimensions greater than or equal to 5. * 1962 – proposes the . * 1962 – becomes the third African American woman to receive a PhD in mathematics. * 1963 – uses his technique of to show that neither the continuum hypothesis nor the axiom of choice can be proven from the standard axioms of set theory. * 1963 – and analytically study the in the continuum limit and find that the governs this system. * 1963 – meteorologist and mathematician published solutions for a simplified mathematical model of atmospheric turbulence – generally known as chaotic behaviour and s or – also the . * 1965 – Iranian mathematician founded theory as an extension of the classical notion of and he founded the field of . * 1965 – Martin Kruskal and Norman Zabusky numerically study colliding in and find that they do not disperse after collisions. * 1965 – and present an influential fast Fourier transform algorithm. * 1966 – presents two methods for computing the in terms of a polynomial in that matrix. * 1966 – presents . * 1967 – formulates the influential of conjectures relating number theory and representation theory. * 1968 – and prove the about the index of s. * 1973 – founded the field of . * 1974 - solves the last and deepest of the , completing the program of Grothendieck. * 1975 – publishes Les objets fractals, forme, hasard et dimension. * 1976 – and use a computer to prove the . * 1981 – gives an influential talk "Simulating Physics with Computers" (in 1980 proposed the same idea about quantum computations in "Computable and Uncomputable" (in Russian)). * 1983 – proves the and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem. * 1985 – proves the . * 1986 – proves . * 1987 – , , , and use iterative modular equation approximations to elliptic integrals and a to compute π to 134 million decimal places. * 1991 – and develop . * 1992 – and develop the , one of the first examples of a that is exponentially faster than any possible deterministic classical algorithm. * 1994 – proves part of the and thereby proves . * 1994 – formulates , a for . * 1995 – discovers capable of finding the ''n''th binary digit of π. * 1998 – (almost certainly) proves the . * 1999 – the full is proven. * 2000 – the proposes the seven of unsolved important classic mathematical questions. 21st century * 2002 – , , and of present an unconditional deterministic algorithm to determine whether a given number is (the ). * 2002 – , Y. Ushiro, , and a team of nine more compute π to 1241.1 billion digits using a 64-node . * 2002 – proves . * 2003 – proves the . * 2004 – the , a collaborative work involving some hundred mathematicians and spanning fifty years, is completed. * 2004 – and prove the . * 2007 – a team of researchers throughout North America and Europe used networks of computers to map . * 2009 – had been by . * 2010 – and solve the . * 2013 – proves the first finite bound on gaps between prime numbers. * 2014 – Project Flyspeck announces that it completed proof of . * 2014 – Using Alexander Yee's y-cruncher "houkouonchi" successfully calculated π to 13.3 trillion digits. * 2015 – solved The * 2015 – found that a quasipolynomial complexity algorithm would solve the * 2016 – Using Alexander Yee's y-cruncher Peter Trueb successfully to 22.4 trillion digits * 2019 – using y-cruncher v0.7.6 calculated π to 31.4 trillion digits. References Category:Math